Micro-structural Modeling Of Extracellular Matrix And Computational Simulation

The extracellular matrix(ECM) is the surrounding environment of most cells and tissues.,which provides structural and biochemical support to cells and tissues. The ECM is a critical factor that modulates cell’s dynamic behavior and intercellular communication. The physical properties of ECM, including the density, stiffness and orientation of fibers, size of pore space etc., greatly influence many cell behaviors, such as cell migration, cell differentiation and tumor cell invasion. It has been proven that the alignment and pore size of ECM is linked to the aggressiveness of tumor cell. Thus, in order to better understand the mechanical and morphological features as well as the mechanism of ECM, a sound theoretically mathematical model that is consistent with the real collagen gel is essential for us to undergo quantitative analysis and research.So far, researchers have done many research about single fiber structure and physical properties of ECM, and has made progress. However, the structure and properties of the whole ECM network has not been well understood. How the micro-structural and mechanical properties of ECM would change under local stress and deformation has also been poor investigated. Many models of the ECM is two-dimensional models, while most three-dimensional models of the ECM only have agreement with real collagen on either mechanical or morphological feature. Heretofore there is hardly a three-dimensional model of ECM that is consistent with both mechanical or morphological feature of the real one.Due to the defects and deficiencies of current research, we developed a three-dimensional collagen fiber network model to simulate the micro structure and mechanics behaviors of the ECM. By setting different parameters, we build several ECM model under different condition and studied the stress-strain relationship as well as the deformation of the ECM under tension. Based on the result of simulation, we found the best-fit parameters and the simulated stress-strain relation of the ECM highly matched the experimental results even in the states of failure. Moreover, we proposed a method to measure the pore size of our model by applying the maximal inscribing sphere method, and compared it to the real ECM. Therefore, we verified the morphological and mechanical correctness of our model. We measured the connectivity of the fiber network by proposing a method to find the connected path in the ECM. We also defined the alignment of the collagen fibers to depict the orientation of fibers in the ECM quantitatively. During tensile simulation, we calculated the pore size, alignment and connectivity of path at different strain so as to analysis the change of structure of the model. We also found the change of alignment offered a very good explanation of the non-linear stress-strain relationship. Our three-dimensional computational fiber network is a vital step toward the understanding of cell dynamic behaviors in the ECM.